An attempt has been made to solve theoretically the problem of the frequencies and intensities of the near infra-red absorption regions of the carbonate group. The assumption, that in the normal state the oxygen nuclei are located at the vertices of an equilateral triangle while the carbon nucleus lies at the center, seems justified by the x-ray investigations of the crystal structure of the group. Using a general potential energy function with three constants under the assumption that the fields of force surrounding the nuclei are central, the normal modes of infinitesimal vibration are determined, yielding four independent frequencies ${\nu }_1$, ${\nu }_2$, ${\nu }_3$, and ${\nu }_4$, of which ${\nu }_4$ is optically inactive. Through the three disposable constants, ${\nu }_1$, ${\nu }_2$, and ${\nu }_3$ may be made to coincide with the three fundamental absorption regions found experimentally by Schaefer and Schubert, and it is found that the optically inactive frequency ${\nu }_4$ agrees closely with the value predicted by Schaefer, Bermuth and Matossi. From a consideration of the change of electric moment, the theoretical intensities are determined. It is found that the relative intensities obtained theoretically agree well with the values determined by Schaefer and Schubert.

• Received 30 July 1928

DOI:https://doi.org/10.1103/PhysRev.32.773